Getal & Ruimte (12e editie) - vwo wiskunde B

'Rekenen met logaritmen'.

vwo wiskunde B 5.4 Logaritmen

Rekenen met logaritmen (8)

opgave 1

Bereken.

1p

a

\({}^{2}\!\log(64)\)

Logaritme (1)
00fi - Rekenen met logaritmen - basis - 0ms

a

\({}^{2}\!\log(64) = {}^{2}\!\log(2^{6}) = 6\)

1p

1p

b

\({}^{2}\!\log(2)\)

Logaritme (2)
00fj - Rekenen met logaritmen - basis - 0ms

b

\({}^{2}\!\log(2) = {}^{2}\!\log(2^{1}) = 1\)

1p

1p

c

\(\log(10)\)

Logaritme (3)
00fk - Rekenen met logaritmen - basis - 0ms

c

\(\log(10) = \log(10^{1}) = 1\)

1p

1p

d

\({}^{8}\!\log(\frac{1}{64})\)

Logaritme (4)
00fl - Rekenen met logaritmen - basis - 0ms

d

\({}^{8}\!\log(\frac{1}{64}) = {}^{8}\!\log(8^{-2}) = -2\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{9}}\!\log(\frac{1}{81})\)

Logaritme (5)
00fm - Rekenen met logaritmen - basis - 0ms

a

\({}^{\frac{1}{9}}\!\log(\frac{1}{81}) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{2}) = 2\)

1p

1p

b

\({}^{\frac{1}{7}}\!\log(49)\)

Logaritme (6)
00fn - Rekenen met logaritmen - basis - 0ms

b

\({}^{\frac{1}{7}}\!\log({}^{\frac{1}{7}}\!\log(49)) = {}^{\frac{1}{7}}\!\log(\frac{1}{7}^{-2}) = -2\)

1p

1p

c

\({}^{3}\!\log(81 \sqrt{3})\)

Logaritme (7)
00fo - Rekenen met logaritmen - basis - 0ms

c

\({}^{3}\!\log(81 \sqrt{3}) = {}^{3}\!\log(3^{4} ⋅ 3^{\frac{1}{2}}) = {}^{3}\!\log(3^{4\frac{1}{2}}) = 4\frac{1}{2}\)

1p

1p

d

\({}^{7}\!\log(7^{4{,}7})\)

Logaritme (8)
00fp - Rekenen met logaritmen - basis - 0ms

d

\({}^{7}\!\log(7^{4{,}7}) = 4{,}7\)

1p

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